G 1/19 – An Overview with a Focus on the Input Side

Complex decisions by the Enlarged Board of Appeal typically require some time until they are digested by interested circles and the Technical Boards of Appeal have applied them in their own decisions. This is particularly true for G 1/19 which deals with the patentability of computer-implemented simulations.

1. What is a Simulation?

In the referring decision (reasons 21), simulation is defined as “an approximate imitation of the operation of a system or process on the basis of a model of that system or process. In the case of a computer-implemented simulation, the model exists only in the computer and the simulation allows the functioning of the modelled system or process to be assessed or predicted”.

Firstly, according to G 1/19 and as generally accepted by computer scientists, a simulation requires a model. Normally, one would understand some complex mathematical calculations, such as partial differential equations or stochastic computation, which help us understand or predict the behaviour of a technical or non-technical (weather, movement of people in a building, economy of a country) system.

For instance, if one has a chemical reactor and temperature sensors are installed on the walls (because it is not possible to install them in the middle of the reactor) of the reactor and a simulation is run which obtains the temperature values from the sensors as input and infers (indirectly measures) based on the temperature values of the sensors the temperature in the middle of the reactor, then this would be considered to be technical. But a “simulation” could be as simple as calculating the average value ( = mathematical model) of the values delivered by two temperature sensors if the assumption that the temperature changes linearly between two positions is part of the model.

Secondly, it is one of the implicit features of a simulation (or any computer program) that it calculates an outputAn input is not necessary since the simulation could be purely based on assumptions.. The output may be destined for a human being or a machine. In some decisions of Technical Boards of Appeal a distinction is made between cognitive data (destined for a human being) and functional data (destined for a machine)G 1/19 does not mention “cognitive data” and does not distinguish between “functional data” and “cognitive data” but mentions “functional data, intended for controlling a technical device” in reasons 92..

Thirdly, it should be mentioned that the terms “model” and “simulation” relate to an external entity/process. In other words, model and simulation are always model and simulation of something external. A calculation in general does not need to have such a relation to an external entity/process which makes clear that not every calculation is a simulation.

Fourthly, one might be inclined to think that another requirement is that a simulation models behaviour over time, i.e. a dynamic processCf. reasons 102 of G 1/19, definition by the Association of German Engineers (VDI). However, there is a class of simulations, called “static simulations” which model a system in a stable (equilibrium) state (snapshot) where time does not play a role, e.g. deformation behaviour of a component under load. Hence, dynamics is not a requirement for a simulation. An example of a dynamic simulation is a simulation for forecasting the weather, while an example of a static simulation is the simulation of stress on a bridge under a constant load which analyzes the bridge’s state at a single moment. In this example, there is no “time” dimension but a “space” dimension illustrating the flow of force through an object. Even some static simulations are inherently in some way dynamic in that, for instance, the deformation of a component could be calculated via the flow of forces through the component. Similarly, consider a noise atlas of an inner city. Sound level is simulated at some points in the city map, while the flow of noise through the buildings will be calculated. There is an own class of static dynamic simulations which generally refers to the use of two complementary simulation approaches – static and dynamic modeling – to analyze a complex system more comprehensively than either method could alone. The primary distinction lies in how the simulation treats the variable of time and system changes.

Hence, it appears difficult to delimit the term “simulating” from terms such as “estimating”, “using an AI model to obtain”, “predicting” or simply “calculating”. In other words, the term “simulation” appears to be inappropriate/unsharp to be delimited from these other words.

Although it has been shown above (see “thirdly”) that not every calculation is a simulation, G 1/19 possibly opens the door to construe “computer-implemented simulation” as broadly as “any calculation based on a mathematical model (referring to an external entity or process) that outputs cognitive data and/or functional data”.

2. Teachings from G 1/19

G 1/19 reminds us that a technical effect must be obtained over the whole scope of the claim (cf. reasons 94 and 95) – a statement which is true for all inventions and goes back to landmark decision T 939/92 of 12 September 1992. A simulation often outputs data to a user, e.g. pedestrians moving through a train station so that the user may gain scientific insight. A design process based on the simulation may output cognitive data how a train station must be built so that it can be evacuated quickly. Even if this train station were built in reality and has the advantage of being able to be evacuated quickly, such advantages cannot be used as a technical effect because the output of the simulation is only data destined for a human being (i.e. cognitive data). In such a case, there would be no technical effect. This means for the output side of a simulation that the claim must exclude that the output is destined for a user. Rather, the output must only be functional data, e.g. data that is used to control a machineAs a side note, in times of AI, a distinction between functional and cognitive data seems to be outdated. Imagine a method for weather simulation (without any sensors or measuring step) which displays the distribution of pressures (cognitive data) to a user so that the user can detect a thunderstorm. The same could be achieved by showing the distribution of pressures to an AI system which is trained to detect thunderstorms..

In a case where no technical effect is achieved or the technical effect is not achieved over the whole scope because only data is output side to a user, G 1/19 basically points to three places (cf. cases #1-3, whilst case #4 may be considered to be a hybrid caseCase #4 deals, for instance, with Graphical User Interfaces which are considered to be technical if they credibly assist a user in performing a technical task by means of a continued and guided human-machine interaction process, cf. T 336/14. since it deals with input and output) where technical effects may be found. G 1/19 acknowledges technicality if in either of these three places there is at least implicitly a link to physical reality. The hardware corresponding to the three places are: sensor – processor – actuator. Either the simulation has a step of acquiring data (e.g. by means of sensors), or the simulation step makes use of a specific hardware (exploits the hardware in an efficient way) or the output of the simulation is used to control an actuator, i.e. the output must be control data (functional data) that is not destined for a human being.

* The Guidelines G-II 3.3 “Mathematical Methods” distinguish between “technical applications” and “technical implementations”. Case # 2A corresponds to “technical implementations”.

** Some voices would not count cryptrographic methods (at least not all cryptographic methods, e.g. T 1326/06) towards case #2B.

Three Places for Technical Effects

Let us start with the ouput, then have a look at computer-implemented processes before we finally have a closer look at the input side.

3.1 Case #3: Output

Expressions such as “further technical use”, “gain scientific knowledge about a technical or natural system…with no limitation to specific technical uses would therefore routinely raise concerns with respect to the principle that the claimed subject-matter has to be a technical invention over substantially the whole scope of the claims”, “technical output may exist as a control signal” , “functional data, intended for controlling a technical device”, “control signals for a printer”, “sending control signals to a technical system” have already attracted a lot of attention.

It is worthwhile mentioning that simulations may be used to design/optimize objects. According to G 1/19 a simulation of an object that outputs an optimized version (e.g. shape) of it in form of control data for controlling a 3D printer which is able to print an optimized version of the object may be considered to be technical. In this case, the mathematical features of the mathematical model may contribute to the technicality of the claimed subject-matter and may be used in the assessment of inventive step (if they are distinguishing features over the closest prior art). Hence, G 1/19 is favourable in terms of design processes as long as they merely output functional data.

Claim 1 below is a process claim. It should be mentioned that a process claim also protects the object that is directly obtained by the process, cf. Art. 64 (2) EPC. In an infringement action, one would have to show that an infringing object has actually been produced by the claimed process. Claim 2 is a product-by-process claim which confers absolute protection to the optimized object.

1. A method of manufacturing an optimized object with a 3D printer,
   comprising obtaining a representation of an object;
   simulating <some mathematical steps: e.g. a wind tunnel simulation using
   a mathematical model> to generate an optimized representation of the object corresponding to an optimized object; and
   providing control signals for a 3D printer which allows the 3D printer to manufacture the optimized object.

2. An optimized object obtained by performing the process, comprising
   obtaining a representation of an object;
   simulating <some mathematical steps: e.g. a wind tunnel simulation using a mathematical model> to generate an optimized representation of the object corresponding to an optimized object; and
   providing control signals for a 3D printer which allows the 3D printer to manufacture the optimized object.

Following G 1/19, the steps of “providing control signals…”, which may be seen as corresponding to printer driver functionality, are necessary to achieve a technical effect.

3.2 Case #2: Computer-implemented Process

Reasons 85 of G 1/19 holds:

“Adaptations to [a] the computer or [b] its operation, which result in technical effects (e.g. better use of storage capacity or bandwidth), are also examples of features that may contribute to inventive step (for a list of examples and references to the relevant board decisions, see T 697/17, Reasons, point 5.2.5). In sum, technical effects can occur within the computer-implemented process (e.g. by [a] specific adaptations of the computer or of [b] data transfer or storage mechanisms) and at the input and output of this process.” ([..] added by author)

Hence, reasons 85 of G 1/19 mentions two sub-cases where technical effects can be found. It holds that adaptations to a) the computer or b) its operation may contribute to inventive step.

3.2.1 Case #2A: Adaptations to the computer (specific hardware)

If the mathematical method is designed to exploit particular technical properties of the technical system on which it is implemented to bring about a technical effect such as efficient use of computer storage capacity or network bandwidth. For instance, the adaptation of a polynomial reduction algorithm to exploit wordsize shifts matched to the word size of the computer hardware is based on such technical considerations and can contribute to producing the technical effect of an efficient hardware implementation of said algorithm.

Another example is assigning the execution of data-intensive training steps of a machine-learning algorithm to a graphical processing unit (GPU) and preparatory steps to a standard central processing unit (CPU) to take advantage of the parallel architecture of the computing platform. The claim should be directed to the implementation of the steps on the GPU and CPU for this mathematical method to contribute to the technical character<^see Guidelines for Examination G-II 3.3 Mathematical Methods, Technical implementations>.

In these cases, a specific hardware and a specific algorithm that exploits the specific hardware is needed. It should be mentioned that also in this case, the output data may be cognitive data since the further use of the data is not relevant.

3.2.2 Case #2B: Adaptations to the operation of the computer or network (e.g. software/mathematical algorithms relating to data transfer or storage mechanisms)

In data transfer/storage, the technical effect is often to reduce the amount of data to be stored/transmitted or to increase the security of the stored data / data transmission.

In T 1326/06, of 30 November 2010, which dealt with the determination of a pair of RSA keys (= a cryptographic method), the Board (3.5.06) apodictically held that

“Methods for encrypting/decrypting or signing electronic messages must be considered technical methods, even if they are essentially based on mathematical methods.”

By contrast, in T 1952/21, of 14 June 2024, the Appellant relied on T 1326/06 to convince the Board (3.5.06) that reinforcement learning (per se, i.e. not restricted to a specific technical task) should be seen in analogy to an encrypting or decrypting method but failed in his efforts. Similarly, in T 702/20, of 7 November 2020, the Appellant tried to convince the Board (3.5.06) that a hierarchical neural network apparatus (per se, i.e. not restricted to a specific technical task) should be seen as a technical subject-matter by referring to T 1326/06. Again, the Board was not convinced by this argument.

In T 1370/18, of 2 December 2021 (5 months after G 1/19), the Board (3.5.07) held that an encoding or compression algorithm contributes to the technical character of the claimed compression method if it is used for the purpose of reducing the amount of data to be stored or transmitted.

“7. Claim 1 specifies a method for encoding a symbol for transmission which achieves the technical effect of reducing the amount of data to be transmitted over substantially the whole scope of the claim. According to established case law, a compression algorithm contributes to the technical character of the claimed compression method if it is used for the purpose of reducing the amount of data to be stored or transmitted (T 107/87, reasons 3; T 650/13, reasons 6.3 and 6.4; T 817/16, reasons 3.11 and 3.12; T 697/17, reasons 5.2.3 to 5.2.5; G 1/19, points 29 and 85). The same holds true for an encoding method with the same technical effect.”

It appears that these effects (e.g. less storage needed, data is stored more safely) are inherently considered to be technical although, as surprising as it may seem, they are essentially based on mathematical methods, cf. T 1326/06.

Further examples would be cost-based optimisation of a query in a relational database system, see T 1003/09 and T 1965/11. Even though data structures used to store cognitive data are not considered to contribute to the technical character beyond the mere storage of data, data structures used for functional purposes are considered to contribute to producing a technical effect (see e.g. T 1194/97 or T 424/03). The technical effects discussed in section 3.2.2 could be called mathematical-technical effects since their technical effects are essentially based on mathematics (without the requirement of a specific hardware). It should be mentioned that these technical effects do not require a restriction on the input or output side and no specific computer hardware is required either.

As a general remark, it should not be forgotten that some of the decisions cited above pre-date G1/19 so that some of the remarks made in these decisions may have to be re-assessed in view of G1/19.

3.3 Case #3: Input – What is an Indirect Measurement?

Regarding the input side, G 1/19 seems to be less restrictive than the output side because it does not require a “further technical use” of the results obtained by the simulation:

99. The calculation of the physical state of an object (e.g. its temperature) is typically part of a measurement method. It is generally acknowledged that measurements have technical character since they are based on an interaction with physical reality at the outset of the measurement method. Measurements are often carried out using indirect measurements, for example, the measurement of a specific physical entity at a specific location by means of measurements of another physical entity and/or measurements at another location (cf. e.g. T 91/10, Reasons, point 5.2.1; T 1148/00, Reasons, point 9). Even though such indirect measurements may involve significant computing efforts, they are still related to physical reality and thus of a technical nature, regardless of what use is made of the results (for a combination of measurements and simulations see e.g. T 438/14).

It is well known that simulations may be used to obtain indirect measurements. So, if one has sensors that measure temperature at some places and a simulation displays temperatures at different places so that the information is determined for a user, then one may still get scientific insight and there is no need for a “further technical use”. It should be mentioned that a simulation based on “measured data” is not sufficient since the simulation method requires an explicit measuring step to achieve a technical effect.

The first decision in which a Board (3.5.07) has acknowledged technicality because of an indirect measurement was T 1422/19 of 19 May 2021. The Board held that “the method does not merely calculate this information from numerical input data but measures ‘raw’ information about a running web browser and processes this information to produce an estimate of a technically meaningful parameter, namely the extent to which a content item displayed within a web page is visible to the user, and on the basis of technical considerations relating to what is possible with an unmodified browser that enforces standard security constraints. Such an indirect measurement is normally of a technical nature.”

In T 660/22, of 20 January 2025, the Board (3.5.06) referred to the expression “regardless of what use is made of the results” and further explained the meaning of indirect measurement by saying:

“13. However, the Board disagrees that all methods of obtaining information about physical reality are measurements within the meaning of G 1/19 (reasons 99).

13.1 The Board considers that any measurement method within that meaning, whether indirect or not, or corresponding device, must be intended to determine a specific and predefined physical quantity. A method of measurement may be called “indirect” if it determines the physical quantity of interest on the basis of the measurement of one or more different physical quantities and a known factual relationship between these quantities.

13.2 Methods comprising the measurement of physical quantities followed by calculations to derive values of interest from the measured values are therefore not indirect measurement methods, unless the calculations correspond to a known factual relationship between the quantities involved and are used to determine the physical quantity of interest.

13.3 For instance, the calculation of a value which does not represent information about physical reality at all, e.g. the price of a refreshment which rises with the measured temperature, is not part of a measurement method.“

A further case where a Board (3.5.01) has acknowledged an indirect measurement is T 1557/20 (cf. T 182/20) of 24 October 2023 which deals with a method for predicting a malfunction of a transformer as an electrical component of a unit. It is worthwhile mentioning that these decisions were the first in which a Board expanded the definition of an indirect measurement from the dimension space (cf. reasons 99 of G 1/19 above: “at a specific location…at another location”) into the dimension time. The Board held:

“However, the Board sees the conditional probability obtained by the method of claim 1 as an indirect measurement of the physical stat of the transformer. This conclusion is based on the following observations:

The claimed method involves taking a measurement of a specific physical entity at a first point in time, and inferring the state of this physical entity (i.e. its probability of failure) at another point in time. This is similar to the example in G 1/19, point 99, where the measurement of a specific physical entity at a specific location is obtained from measurements of another physical entity and/or measurement at another location.

The estimate of the future state of the component credibly reflects reality. The Board considers this an essential factor in deciding whether the calculated numerical data can be seen as an indirect measurement.

Arbitrary or speculative models and algorithms that are not grounded in reality are not capable of predicting the physical state or property of a real physical entity. Such abstract calculations could not be regarded as (indirect) measurements.“

A further example where an indirect measurement has been acknowledged is T 591/23 (Board 3.2.03) of 11 March 2025. It determines whether a first sensor works properly by using measurements of the first sensor and a second sensor.

For the sake of completeness, yet another example of an indirect measurement can be found in the Guidelines for Examination at the EPO at G-VII 5.4.2.4. The example is based on T 438/14 and deals with a method for determining a risk of condensation using an infrared camera.

In T 1741/22, of 26 June 2024, the Board (3.5.05) held that the mere generation of further data from measurement already collected from the human body is not a technical effect. The claim at issue relates to a system for analysing glucose monitoring data indicative of a glucose level. The system receives continuously glucose monitoring data (i.e. already measured data), determines a plurality of minimum glucose values and/or a plurality of maximum glucose values and displays signals representing the plurality of minimum glucose values and/or the plurality of maximum glucose values. The method neithers contains a measuring step and merely outputs (cognitive) data that may be analysed by a physician. The overall method cannot be considered to be a direct or indirect measurement and is also not linked to physical reality on the output side since it merely displays cognitive data. This decision is in contradiction to T 2681/17 and G-II 3.3 of the Guidelines for Examination at the EPO. Referring to the example in the Guidelines of “providing a medical diagnosis by an automated system processing physiological measurements” as an example of technical contributions of a mathematical method, the Board held this example to be “clearly erroneous” since “providing medical diagnosis – whether done by a physician or by an automated system – is devoid of any technical character (see e.g. G 1/04, Reasons 5.3 and 6.3)”. In the eyes of the author of this article, decision T 1741/22 jeopardizes the patentability of AI based medical diagnosis systems (even if they contain a measuring step). The author of this article is of the opinion that Reasons 5.3 has been misinterpreted by the Board. Reasons 5.3 merely says that the deductive medical or veterinary decision phase is a purely intellectual exercise. In order to be technical, the method necessarily further has to include preceding steps of a technical nature. The author of this article is of the opinion that Reasons 5.3 cannot be used to say that providing medical diagnosis is devoid of any technical character. For instance, if the diagnosis step is based on a trained AI which is shown pictures of the skin of a patient and can then determine whether the patient has skin cancer or not (the AI has been trained by being shown pictures of the skin of patients some of which shows skin cancer and others show healthy skin), then this diagnosis step is not a purely intellectual exercise but based on image processing and thus of a technical nature.

Measurements – be they indirect or direct – may be seen to represent a link to physical reality and may therefore be considered to be technical. The question arises what is an indirect measurement and how it can be delimited from a direct measurement.

“A priori, it is noted that the distinction between a direct and an indirect measurment is not as sharp as it may seem. Arguably, most (if not all) measurements must be seen as indirect to some degree. While the measurement of a person’s height with a yardstick held next to them might appear as a reasonably direct measurement, already measuring temperature with a mercury thermometer is indirect insofar as the expansion of the mercury with rising temperature is mapped to a proportional increase in temperatureMüller, M., “Patenting Measurements”, Journal of Intellectual Property Law and Practice, 2024, Vol. 20, Issue 4, April 2025, Pages 275-280.”

There appears to be a grey zone between direct measurements and indirect measurementsAs a side note, indirect measurements – in mathematics sometimes also referred to as “inverse problems” – play an important role in medicine, such as in electromagnetic tomography or ultrasound imaging which could be described as follows. The less a measurement relies on a mathematical model (or the more the measurement is tied to physical reality), the more it can be considered to be a direct measurement. An example would be a method of determining a shortest path to a destination comprising receiving a GPS signal indicating a current position (measurement) of a vehicle.

Typically, a navigation system in a vehicle is based on a mathematical model (e.g. a graph model in which the localities (cities, towns, villages, etc) are the vertices and the distances (roads) between the localities are the edges and e.g. Dijkstra’s algorithm may be used to find the shortest path from a current position to a destination). In order to find the shortest path, the method determines the shortest path using Dijkstra’s algorithm and adds up the distances from the edges. This method could be considered to be an indirect measurement. By contrast, in a direct measurement, a satellite or a land surveyor would have to measure the individual distances each time anew which is quite time consuming. However, a land surveyor travelling from the current position to the destination to measure the shortest distance would possibly remark that new streets have been built or others have been removed so that the graph model was not up-to-date which reminds us of the fact that “the map is not the territory”Müller, M. “Issues in patenting ‘artifical intelligence’ from an EPO perspective”, Journal of Intellectual Law and Practice, Vol. 19, Issue 3, March 2024, Pages 201-202, Section 4.3, Footnote 87: The phrase was coined by Alfred Korzybski to emphasize that a representation of reality is not the same as reality itself. It explains that models, including maps, are abstractions that simplify and generalize to make things easier to understand, but they inherently lose some of the complexity and nuances of the original. and no model can be as good as reality which can be seen as a justification for a discrimination between model and reality and thus for the approach taken in G1/19 which excludes computer-implemented simulations without any direct or indirect link to physical reality from patentability.

The fact that measurements are taken at some point does not mean that the overall method can be seen as a direct or indirect measurement. Imagine a humanoid robot that is able to interact with a human being. When the human being shakes its hand, then the humanoid having sensors in its hand will measure temperature, humidity of the human being’s hand and the human being’s heartbeat. Based on these measurements, the humanoid’s AI will determine the human being’s mood and the humanoid will greet the human being with the words: “Hello xy, I feel you are in a good/bad mood today.” In such a case, a technical effect may not be achieved, since determining the mood of a person is likely considered to be a non-technical problem. The fact that some measurements take place is not enough that the overall process may be considered to be an indirect measurement. By contrast, if the humanoid’s AI would be able to determine the blood pressure of the person it shakes hand based on measured input parameters, then this could be considered to be technical. Should the humanoid robot provide a medical diagnosis, this might not be a techical method following T 1741/22 (see above).

Another example may be measuring variable ambient light conditions in a disco, using a mathematical model to select from a list a picture to be displayed which best embodies the mood set by the ambient lighting.Example taken from “Tackling the future: Cross-field inventions in additive manufacturing”, Online Presentation at EPO Academy, 1 October 2024 While the method obtains measurements as input, the overall method may neither be seen as an indirect measurement nor a direct measurent and does not achieve a technical effect either.

Yet another example could be a method comprising a step of measuring barometric pressure at different weather stations throughout a territory and forecasting the weather by using numerical simulation.

The Boards of Appeal will have to determine whether a claimed method as a whole can still be considered to be an indirect measurement. While forecasting the weather for tomorrow may still be seen as an indirect measurement, forecasting the weather in a month appears to be a matter of speculation. In such cases, the model has to be analysed carefully and performance data (benchmark data) indicating e.g. the confidence of the model or the approximation of reality (accuracy) may be adduced as evidence to show that the method qualifies as an indirect measurement. Regarding accuracy, the Guidelines for Examination G-II 3.3.2 expound:

“Whether a simulation contributes to the technical character of the claimed subject-matter does not depend on the quality of the underlying model or the degree to which the simulation represents reality.

However, the accuracy of a simulation is a factor that may influence an already established technical effect going beyond the mere implementation of the simulation on a computer. It may be that an alleged improvement is not achieved if the simulation is not accurate enough for its intended technical purpose. This may be taken into account when formulating the objective technical problem (Art. 56) or assessing sufficiency of disclosure (Art. 83) (see F-III,12). Conversely, a technical effect may still be achieved by a method where certain simulation parameters are inaccurate but sufficient for the method’s intended technical use.“

Hence, the accuracy of a model may determine whether a claimed method may still be considered to be an indirect measurement or not, i.e. whether the objective technical problem of providing an indirect measurement is solved or not.

The Boards of Appeal will have to draw a line based on a case-by-case basis in consideration of all aspects, e.g. the quality of the model, which of these cases may still be considered to be an indirect measurement and which do not meet this requirement.

In summary, for a mathematical method that merely outputs cognitive data (without controlling a machine), technicality may be acknowledged if the claim is restricted on the input side in form of a direct or indirect measurement. Restricting the claim on the process side may only be possible in exceptional cases (use of specific hardware) and restricting it on the output side is impossible.

4. Conclusion

This article has approached the term “computer-implemented simulation” and how a computer-implemented simulation may be delimited from any other calculation. G 1/19 teaches us where we can find technical effects if they are not apparent, for example, if it appears that merely (cognitive) data is output to a user. The article has had a closer look at the input side which will become more important and the discussion will remain topical, given the fact that G 1/19 has raised the bar on the patentability of computer-implemented simulations, but suggested that it might be overcome in view of an indirect measurement, without having to limit the claim, explicitly and implicitly, to a particular use of the results.Müller, M., “Patenting Measurements”, Journal of Intellectual Property Law and Practice, 2024, Vol. 20, Issue 4, April 2025, Pages 275-280 The Boards of Appeal have already and will continue to draw a fine line between which claimed subject-matter may still qualify as an indirect measurement and which subject-matter may not.

5. Acknowledgement

The author thanks Martin Müller for some valuable feedback on a draft of this article.

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